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Integers, Pi, and Number Lines.
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mathsquid:
None of this makes any sense.
tggzzz:

--- Quote from: mathsquid on June 30, 2022, 08:40:22 pm ---None of this makes any sense.

--- End quote ---
K

All will become clear if you look at the other topic starter emitted by the OP.

TL:DR your statement is correct.
TimFox:
19th century mathematics is something that happened to other people.
eugene:

--- Quote from: Peter Taylor on June 29, 2022, 11:01:29 pm ---In classic education, we are taught that a number line contains an infinite number of irrational numbers between each integer. I will show that it should contain only integers.

--- End quote ---

When I was taught about the number line in grade school we also learned about different number systems. Specifically real numbers, integers, and so-called natural numbers. Do recall that part of your classical education?


--- Quote ---dy / dx is never evaluated because dx is infinitely small and zero.

--- End quote ---

Neither dy or dx are ever zero, but they do approach zero. In classical education the concept is introduced in the form of a limit.


--- Quote ---When working with Fourier Transforms for example, the terms are introduced into a formulae as a pair to help solve it, and then disappear at the end without ever being evaluated.

--- End quote ---


I don't know what you mean by that. Nothing disappears without being evaluated. I assure you that Mr. Fourier was not a fool.


--- Quote ---The imaginary number "square root -1" is never evaluated, but introduced into a formulae at the start to help solve it, and disappears at the end.

--- End quote ---

Again, I don't understand what you mean. If you're working with mathematical statements and surprised that terms have disappeared, then either you lack a basic understanding of the math or you're doing it wrong.


--- Quote ---Pi also is not evaluated, but remains the ratio of the circumference of a circle to its radius.

--- End quote ---

I evaluate pi regularly.


--- Quote ---"Square root 2" likewise is not evaluated, but remains a question: "What value multiplied by itself equals 2 ?".

--- End quote ---

Likewise, I evaluate sqrt(2) regularly. The fact that I can't write it down with a finite number of decimal digits is nothing more than a minor inconvenience.


--- Quote ---These are termed irrational "numbers", having no exact value.

--- End quote ---

Yes they do! Who told you they don't have exact values? Don't trust that person to teach you math. They must be incurably stupid!


--- Quote ---But these are not numbers, or values, but questions, or formulae.

--- End quote ---

No, they're numbers, just like 1 or 10.25. Again, don't trust the person that told you they aren't.


--- Quote ---If we remove all these non-numbers, or questions, or ratios, or any unevaluated formulae from our number line, we are left only with integer numbers.

--- End quote ---

If we remove those numbers from the set of real numbers then we'll have a different set of numbers. You can ponder that set all you want, but I don't see how it will be useful to me. I need all the reals to get much of my work done.


--- Quote ---So, a number line should contain only integer numbers.

--- End quote ---

Now we're back to the elementary school concepts of real numbers, integers, and natural numbers. Nobody is stopping you from working with only the set of integers. If you want to talk about it with someone you might find a third grade math teacher. That's where I learned this stuff.

EDIT: the campaign to stop people from driving while drunk is for the safety of others. Posting while high doesn't present a safety problem, but it does make you look like a fool.

So don't post while high.
SiliconWizard:
When you see that: https://equitablemath.org/
everything becomes possible.
 :-DD
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